CAT 2022 Slot 3 QA Q13 Ratio, Mixtures & Averages

Question 13 of the Quantitative Ability (QA) section, CAT 2022 Slot 3, with CAT's official answer and a worked solution.

Consider six distinct natural numbers such that the average of the two smallest numbers is 14, and the average of the two largest numbers is 28. Then, the maximum possible value of the average of these six numbers is
  1. A
    22.5
  2. B
    23.5
  3. C
    24
  4. D
    23

Answer: (A) 22.5 Ratio, Mixtures & Averages MCQ

Solution

  1. Smallest two sum to 28, largest two sum to 56; to maximise the total, make the middle two as large as possible.
  2. The middle two must be below the smaller of the top two. Keep the top two as close as possible while distinct: 27 and 29.
  3. Then the middle two are at most 26 and 25 (the bottom two, e.g. 13 and 15, are smaller).
  4. Total \(=28+51+56=135\), average \(=22.5\).

Same concept in other years

See every question on Maximise or minimise one value given an average and distinct/bounded others.

More Ratio, Mixtures & Averages questions from CAT

All 84 Ratio, Mixtures & Averages questions asked since 2017.